Alright Tetrahedron

Geometry Level 5

In a tetrahedron ABCD,ABCD, the lengths of AB,AB, AC,AC, and BDBD are 6,6, 10,10, and 1414 respectively. The distance between the midpoints MM of ABAB and NN of CDCD is 4.4. The line ABAB is perpendicular to AC,AC, BD,BD, and MN.MN. The volume of ABCDABCD can be written as ab,a\sqrt{b}, where aa and bb are positive integers, and bb is not divisible by the square of a prime number. What is the value of a+ba+b?

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